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math.AG2024
Mori dream singular surfaces
Antonio Laface, Alex Massarenti, William D. Montoya
We take a first step towards the classification of singular Mori dream surfaces. We prove that if the Picard lattice of a singular surface is Mori dream, then the surface…
math.AG2024
The moduli space of genus Fano -folds with two -points: rationality and K-stability
Joseph Malbon, Alex Massarenti, Francesco Zucconi
Let be the moduli space of genus Fano -folds with two terminal quotient singularities of type . We prove that $\mathca…
math.AG2024
Rational points on even dimensional Fermat cubics
Alex Massarenti
We show that even dimensional Fermat cubic hypersurfaces are rational over any field of characteristic different from three by producing explicit rational parametrizations given by…